Under the curious minds of the ancient Greeks, beginning with Pythagoras, who brought with him new concepts he learned during his time in Egypt, mathematics rose to a highly evolved level of theoretical mathematics, which ushered in a golden age of math.

But, the Greek’s role in mathematics ended, quite literally, with Archimedes, who was killed by a Roman soldier during the Siege of Syracuse in 212 BC. Under the rule of Rome, mathematics entered a dark age, and for a couple different reasons.

The main reason was that Romans simply weren’t interested in mathematics (they were more concerned with world domination), and secondly, because Roman numerals were so unwieldy, they couldn’t be used for anything more complicated than recording the results of calculations. Romans did all their calculating on a counting board, which was an early version of an abacus. And because of that Roman mathematics couldn’t, and didn’t, go far beyond adding and subtracting. Their use of numbers was good for nothing more than a simple counting system. The Romans' use of numbers was no more advanced than the notches on the Ishango Bone. There’s a good reason there are no famous Roman mathematicians.

The next big advance (and it was a huge advance) in the world of numbers and mathematics came around 500 AD in India. It would be the most revolutionary advance in numbers since the Sumerians invented math. The Indians invented an entirely new number: zero.

Under Hinduism, the Indians possessed concepts such as Nirvana and eternity. These are some very abstract concepts that need some abstract math to help describe them. Take for instance a Rajju. A Rajju is the distance that a deity can fly in a six-month period. Or a Palya, which is the length of time it would take to build a cube of lamb’s wool 10-km high if you were to lay one strand of lamb’s wool every century. Try expressing that idea with Roman numerals.

The Indians needed a way to express very large numbers, and so they created a method of counting that could deal with very large numbers. It was they who created a different symbol for every number from one to nine. They are known today as Arabic numerals, but they would more properly be called Indian numbers, since it was the Indians who invented them. The Indians have been using “Arabic” numbers them since about 500 BC.

Once zero was invented it transformed counting, and mathematics, in a way that would change the world. Zero is still considered India’s greatest contribution to the world. For the first time in human history the concept of nothing had a number.

Zero, by itself, wasn’t necessarily all that special. The magic happened when you paired it with other numbers. With the invention of zero the Indians gained the ability to make numbers infinitely large or infinitely small. And that enabled Indian scientists to advance far ahead of other civilizations that didn’t have zero, due to the extraordinary calculations that could me made with it. For example, Indian astronomers were centuries ahead of the Christian world. With the help of the very plastic and fluid Arabic numbers, Indian scientists worked out that the Earth spins on its axis, and that it moves around the sun, something that Copernicus wouldn’t figure out for another thousand years.

The next big advance in numbers, the invention of fractions, came in 762 AD in what is now Baghdad — and what was then Persia. The Persians were Muslims, and it was their adherence to the Koran and the teachings of Islam that led to the invention of fractions.

The Koran taught that possessions of the deceased had to be divided among their descendants. Unlike Christianity at the time, Islam — which was scarcely 100 years old at the time — divided belongings among women as well as men. But women got a lesser share. Working all of that out required fractions. But prior to 762 AD they didn’t have a system of mathematics sophisticated enough to do a very proper job. Enter Arabic numbers.